The light scalar mesons as tetraquarks

Abstract

We present a numerical solution of the four-quark Bethe–Salpeter equation for ground-state scalar tetraquarks with JPC=0++. We find that the four-body equation dynamically generates pseudoscalar-meson poles in the Bethe–Salpeter amplitude. The resulting tetraquarks are genuine four-quark states that are dominated by pseudoscalar meson–meson correlations. Diquark–antidiquark contributions are subleading because of their larger mass scale. In the light quark sector, the sensitivity of the tetraquark wave function to the pion poles leads to an isoscalar tetraquark mass Mσ∼350 MeV which is comparable to that of the σ/f0(500). The masses of its multiplet partners κ and a0/f0 follow a similar pattern. This provides support for a tetraquark interpretation of the light scalar meson nonet in terms of ‘meson molecules’.